Math 227
Problems, Solutions, Handouts
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- Course Outline
[
html,
pdf
]
-
Mathematics Department Exam Database
- Tables of formulae
- Trig identities.
[ pdf ]
- Derivatives.
[ pdf ]
- Indefinite integrals.
[ pdf ]
- Properties of exponentials and logarithms.
[ pdf ]
- Taylor Expansions.
[ pdf ]
- Old Math 227 exams
- April 2012
[ questions
, answers
, solutions
]
- April 2011
[ questions
, answers
, solutions
]
- April 2009
[ questions
, answers
, solutions
]
- April 2006
[ questions
, answers
, solutions
]
- April 2005
[ questions
, answers
, solutions
]
- Final exam: Thursday, April 11, 8:30-11:00
in room MATH 225.
- Review session: Tuesday, April 9, 10:00-12:00
in room MATH 103.
Tests
Problem Sets
- Problem Set I (Due Wednesday, January 9)
[
questions
, solutions
]
- Problem Set II (Due Wednesday, January 16)
[
questions
, solutions
] Due date delayed to Friday, January 19.
- Problem Set III (Due Wednesday, January 23)
[
questions
, solutions
]
- Problem Set IV (Due Wednesday, January 30)
[
questions
, solutions
]
- Problem Set V (Due Wednesday, February 13)
[
questions
, solutions
] Question #3 reworded.
- Problem Set VI (Due Wednesday, February 27)
[
questions
, solutions
]
- Problem Set VII (Due Wednesday, March 13)
[
questions
, solutions
]
- Practice Problems Involving Limits of Integration (Not to be handed in)
[
questions
, solutions
]
- Problem Set VIII (Due Wednesday, March 20)
[
questions
, solutions
]
- Problem Set IX (Due Wednesday, March 27)
[
questions
, solutions
]
- Problem Set X (Never due)
[
questions
, solutions
]
Notes
- Properties of Derivatives of Vector Valued Functions
[
pdf
]
- The Astroid
[
pdf,
applet
]
- Parametrizing Circles
[
pdf
]
- A Compendium of Curve Formulae
[
pdf
]
- Skateboarding in a Culvert
[
pdf
]
- Review of Ordinary Differential Equations
[
pdf
]
- The Damped Pendulum
[
pdf,
applet
]
- 3d Coordinate Systems
[
pdf
]
- Flux Formulae
[
pdf
]
- Flux Integral Example
[
pdf
]
- Vector Identities
[
pdf
]
- Divergence Theorem and Variations
[
pdf
]
- Proof that "a . b x c = a x b . c"
[
pdf
]
- Buoyancy
[
pdf
]
- Stokes' Theorem
[
statement and proof
, example
]
- More About Which Vector Fields Have Curl Zero
[
pdf
]
- The Physical Significance of div and curl
[
short, simple, version ,
longer, more involved, version
]
More Notes
- Complex Numbers and Exponentials
[
pdf
]
- Hyperbolic Trig Functions
[
pdf
]
- Quadric Surfaces
[
pdf
]
- Vectors and Geometry in Two and Three Dimensions
[
pdf
]
- Precession of the Perihelion of Mercury
[
pdf,
applet
]
- Numerical Approximate Solutions to ODE's
- Simple ODE Solvers - Derivation
[ pdf ]
- Simple ODE Solvers - Error Behaviour
[ pdf ]
- Richardson Extrapolation
[ pdf ]
- The RLC Circuit
[
pdf
]
- Rigid Body Motion
- Torque
[ pdf]
- A Summary of Rigid Body Formulae
[ pdf ]
- Euler Wobble
[ pdf ]
- The Chain Rule
[
pdf
]
- The Contraction Mapping Theorem
[
pdf
]
- Circulation around a small circle
[
pdf
]
- The Divergence/Stokes' theorems and partial differential equations
[
The Heat Equation ,
Faraday's Law ,
Poisson's Equation
]
- Integration on Manifolds
[
notes ,
problem solutions
]
Transparencies used in class
- The Divergence Theorem
[
pdf
]
- The Boat
[
pdf
]
- The Paddle Wheel
[
pdf
]